It is already known to supply secondary air to the exhaust gas of an internal combustion engine after a cold start and when the lambda control is not yet operationally ready. The secondary air is blown in between the outlet valves of the engine and a catalytic converter. The exothermal reaction of the secondary air with the hot exhaust gases and the further oxidation in the catalytic converter lead to an accelerated heating of the catalytic converter and therefore to an improved conversion of toxic substances in the warm-up phase after a cold start of the engine. Such a system is disclosed in the article of Zahn et al entitled "The Emission Control System of the New 300SL-24 and 500SL--Structure and Function", published in the Motortechnische Zeitschrift 50 (1989), Volume 6, page 249. Statutory requirements furthermore provide for monitoring of the supply of secondary air. The California Environmental Authority (CARB) characterizes the quantity of secondary air as being critical for minimizing the emission of toxic substances in the case of a cold start. Here, and for monitoring the function, the suggestion is made that the supply of secondary air be activated briefly and that the reaction of the lambda control be evaluated. The supply of the secondary air during the diagnosis should be reduced in order to keep a possible deterioration of the conversion of toxic substances as small as possible. A reduction of the rpm of the secondary air pump is suggested for the case wherein the secondary air pumps are driven electrically.